"My friend says that he loves you a lot."
Translation:Mi amigo dice que él te quiere mucho.
I missed this too, but once I read into it more, I realized that the friend could be a female speaking about another friend who is male.
I think both "Mi amigo dice que el te quiere mucho" and "Mi amiga dice que el te quiere mucho" are correct answers. They have different meanings: in the first sentence, the person who loves the person addressed a lot could either be the friend himself or a third (male) person. In the second sentence, only the latter meaning is possible.
Is there a rule about dicer que? I use it with que but I'm sure I've seen sentences with que missing?
Te can be a direct or indirect object pronoun. In this sentence quiere or ama /loves is referring to a direct object 'you'. When the person is an object and not a subject in the sentence we use pronouns and have the option of adding for clarification purposes the prepositional phrase 'a ella' for example.